Rothe–Hagen identity

In mathematics, the Rothe–Hagen identity is a mathematical identity valid for all complex numbers (x, y, z) except where the denominators vanish:

\sum_{k=0}^n\frac{x}{x+kz}{x+kz \choose k}\frac{y}{y+(n-k)z}{y+(n-k)z \choose n-k}=\frac{x+y}{x+y+nz}{x+y+nz \choose n}.

It is a generalization of Vandermonde's identity, and is named after Heinrich August Rothe and Johann Georg Hagen.

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